The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 237 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Distribution of first digits (Benford's Law) Digit 1 2 3 4 5 Probability 0.301 0.176 0.125 0.097 0.079 Digit 6 7 8 9 Probability 0.067 0.058 0.051 0.046 First digits in allegedly fraudulent checks First digit 1 2 3 4 5 6 7 8 9 Frequency 36 32 45 26 23 36 15 17 7 1.) Because these data are meant to prove that someone is guilty of fraud, what would be an appropriate level of significance when performing a goodness-of-fit test? Use α= _____? 2. What is the test statistic χ2 = _____? 0 (Round to three decimal places as needed. 3.What is the P-value of the test P-value=_____? (Round to three decimal places as needed.)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The
Distribution of first digits (Benford's Law)
|
Digit
|
1
|
2
|
3
|
4
|
5
|
|
|---|---|---|---|---|---|---|
|
Probability
|
0.301
|
0.176
|
0.125
|
0.097
|
0.079
|
|
|
Digit
|
6
|
7
|
8
|
9
|
|
|
|
Probability
|
0.067
|
0.058
|
0.051
|
0.046
|
First digits in allegedly fraudulent checks
|
First digit
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|---|---|---|---|---|---|---|---|---|---|
|
Frequency
|
36
|
32
|
45
|
26
|
23
|
36
|
15
|
17
|
7
|
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